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How Do You Make a Density Histogram?

Published in Data Visualization 3 mins read

A density histogram visually represents the distribution of data, showing the relative frequency of data points within specified intervals. Unlike a standard histogram displaying frequencies, a density histogram displays density, making it easier to compare distributions with different sample sizes or bin widths.

Constructing a Density Histogram

To create a density histogram, follow these steps:

  1. Determine your data: Begin with a numerical dataset you want to visualize.

  2. Choose class intervals (bins): Divide the range of your data into several equal-width intervals. The number of bins influences the histogram's appearance; too few bins obscure detail, while too many create a noisy, uneven representation.

  3. Calculate the frequency for each bin: Count how many data points fall within each interval.

  4. Calculate the density for each bin: For each bin, calculate its density using the formula: h(x) = fᵢ / (cᵢ - cᵢ₋₁) where:

    • fᵢ is the frequency (number of data points) in the ith bin.
    • cᵢ is the upper boundary of the ith bin.
    • cᵢ₋₁ is the lower boundary of the ith bin.

  5. Draw the rectangles: Draw a rectangle for each bin. The width of the rectangle is the bin width (cᵢ - cᵢ₋₁), and the height is the calculated density h(x). This ensures the area of each rectangle represents the proportion of data points in that bin. The total area under the density histogram will always equal 1.

Example:

Let's say we have data points: 2, 3, 4, 4, 5, 5, 5, 6, 7, 8. We can create bins of width 1: [2-3), [3-4), [4-5), [5-6), [6-7), [7-8), [8-9).

  • Bin [2-3): Frequency (fᵢ) = 1, Density = 1/(3-2) = 1
  • Bin [3-4): Frequency (fᵢ) = 1, Density = 1/(4-3) = 1
  • Bin [4-5): Frequency (fᵢ) = 2, Density = 2/(5-4) = 2
  • Bin [5-6): Frequency (fᵢ) = 3, Density = 3/(6-5) = 3
  • Bin [6-7): Frequency (fᵢ) = 1, Density = 1/(7-6) = 1
  • Bin [7-8): Frequency (fᵢ) = 1, Density = 1/(8-7) = 1
  • Bin [8-9): Frequency (fᵢ) = 1, Density = 1/(9-8) = 1

You would then draw rectangles with widths of 1 and heights corresponding to the calculated densities.

Software Tools

Many statistical software packages (like R, Python with libraries such as Matplotlib and Seaborn, and others) simplify the process of creating density histograms. These tools often allow for customization of bin widths and the addition of features like overlaid normal curves for distribution comparisons. [Refer to the provided YouTube links for visual demonstrations.]

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